Amatuer question about electron drift speed.

[wil3]

I'm teaching myself some physics, and I am having some difficulty with the concept of drift speed. My book derived the time between collisions using

ma=Eq

and then substituting the acceleration into the first equation of kinematics and solving for v(final) as the drift speed. The time it took for the average velocity to increase from zero to the drift speed was equal to the time between collisions.

My question is: Why do the electrons cease to accelerate above the drift speed? I am aware that the drift speed is an average, but it seems like a constant emf in a circuit would cause the average velocity to gradually grow. Even if each elastic collision resets the velocity of the progenitor electron to zero, it seems that, with a constant field, eventually the circuit "runs out" of electrons traveling below the drift speed.

So, why don't the electrons keep accelerating in a circuit? Thank you very much for any help.

 

[Bob S]

See Wiki on electron mobility at

http://en.wikipedia.org/wiki/Electron_mobility

As the electron velocity increases in a drift field, the inelastic electron (and hole) collisions increase to the point that the energy lost per cm equals the energy gained, so the velocity does not increase further, unless the drift field is increased. Conductors never "run out" of conduction electrons. There are roughly 6 x 10²³ conduction electrons per gram molecular weight in a conductor. An average conduction electron drift velocity of 1 cm/sec in copper corresponds to a current of about 13,000 amps per cm².

Bob S

 

[sophiecentaur]

Even in a vacuum, an electron will only reach a speed such that its Kinetic Energy is equal to its charge times the voltage across the gap. The field across a conductor is very small, too, so one wouldn't expect high velocity. (For a perfect conductor the field would be zero, even.) The resistive effect of interactions and the voltage drop across the conductor are, of course, related and must tie in with the limit to the acquired (additional, mean) electron velocity due to 'collisions'. Remember, the mean square (thermal) velocity of the electrons is pretty high in comparison with the drift speed.